{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Training Models - Intro"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Linear Regression\n",
    "\n",
    "* y = theta0 + (theta1 * x1) + (theta2 * x2) + ...\n",
    "*   = h(theta)(x) \n",
    "*   = theta^T (dot) x --- theta^T = theta vector, transposed (row instead of col)\n",
    "\n",
    "* Training a model = finding theta that minimizes error function (ex: MSE)\n",
    "\n",
    "![alt text](MSE-cost-function-linear-regression.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Normal Equation: finds theta that minimizes cost function"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f9856cd80b8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# generate some data\n",
    "import numpy as np\n",
    "X = 2 * np.random.rand(100, 1)\n",
    "y = 4 + 3 * X + np.random.randn(100, 1)\n",
    "\n",
    "%matplotlib inline\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "plt.scatter(X,y)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[ 3.58859665]\n",
      " [ 3.41876053]]\n"
     ]
    }
   ],
   "source": [
    "# find theta. \n",
    "# 1) use NumPy's matrix inverse function.\n",
    "# 2) use dot method for matrix multiply.\n",
    "\n",
    "X_b = np.c_[np.ones((100, 1)), X] # add x0 = 1 to each instance\n",
    "theta_best = np.linalg.inv(X_b.T.dot(X_b)).dot(X_b.T).dot(y)\n",
    "\n",
    "# results:\n",
    "print(theta_best) # compare to generated data: y = 4 + 3x + noise"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[  3.58859665]\n",
      " [  7.00735719]\n",
      " [ 10.42611772]]\n"
     ]
    },
    {
     "data": {
      "image/png": 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OLJ0u4B+cc6vMbASw0swedM6tCahtIiISoJJ7+M65zc65VZm/7wLWAoVvWCsi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\nIhITCnwRkZhQ4IuIxIQCX0QkJv4/thaqLyvY4UAAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f9825c6d630>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# make some predictions\n",
    "\n",
    "X_new     = np.array([[0],[1],[2]])\n",
    "X_new_b   = np.c_[np.ones((3, 1)), X_new] # add x0 = 1 to each instance\n",
    "y_predict = X_new_b.dot(theta_best)\n",
    "print(y_predict)\n",
    "\n",
    "# then plot\n",
    "\n",
    "plt.plot(X_new, y_predict, \"r-\")\n",
    "plt.plot(X, y, \"b.\")\n",
    "plt.axis([0, 2, 0, 15])\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "intercept & coefficient:\n",
      " [ 3.58859665] [[ 3.41876053]]\n",
      "predictions:\n",
      " [[  3.58859665]\n",
      " [  7.00735719]\n",
      " [ 10.42611772]]\n"
     ]
    }
   ],
   "source": [
    "# Scikit equivalent\n",
    "from sklearn.linear_model import LinearRegression\n",
    "lin_reg = LinearRegression()\n",
    "\n",
    "lin_reg.fit(X,y)\n",
    "print(\"intercept & coefficient:\\n\", lin_reg.intercept_, lin_reg.coef_)\n",
    "print(\"predictions:\\n\", lin_reg.predict(X_new))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Gradient Descent"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[ 3.58859665]\n",
      " [ 3.41876053]]\n"
     ]
    }
   ],
   "source": [
    "# Gradient Descent - Batch\n",
    "# (Batch: math includes full training set X.)\n",
    "\n",
    "# need to find partial derivative (slope) of the cost function\n",
    "# for each model parameter (theta).\n",
    "\n",
    "theta_path_bgd = []\n",
    "\n",
    "eta = 0.1 # learning rate\n",
    "n_iterations = 1000\n",
    "m = 100\n",
    "\n",
    "theta = np.random.randn(2,1) # random initialization\n",
    "\n",
    "for iteration in range(n_iterations):\n",
    "    gradients = 2/m * X_b.T.dot(X_b.dot(theta) - y)\n",
    "    theta = theta - eta * gradients\n",
    "    theta_path_bgd.append(theta)\n",
    "    \n",
    "print(theta)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[ 3.6036273 ]\n",
      " [ 3.44079196]]\n"
     ]
    }
   ],
   "source": [
    "# Gradient Descent - Stochastic\n",
    "# Stochastic: finds gradients based on random instances\n",
    "# adv: better for huge datasets\n",
    "# dis: much more erratic than batch GD \n",
    "#      -- good for avoiding local minima\n",
    "#      -- bad b/c may not find optimum sol'n\n",
    "\n",
    "# simulated annealing helps. (gradually reduces learning rate)\n",
    "\n",
    "theta_path_sgd = []\n",
    "\n",
    "n_epochs, t0, t1 = 50, 5, 50 # learning schedule hyperparameters\n",
    "\n",
    "def learning_schedule(t):\n",
    "    return t0 / (t + t1)\n",
    "\n",
    "theta = np.random.randn(2,1) # random initialization\n",
    "\n",
    "for epoch in range(n_epochs):\n",
    "    for i in range(m):\n",
    "        random_index = np.random.randint(m)\n",
    "        xi = X_b[random_index:random_index+1]\n",
    "        yi =   y[random_index:random_index+1]\n",
    "\n",
    "        gradients = 2 * xi.T.dot(xi.dot(theta) - yi)\n",
    "\n",
    "        eta = learning_schedule(epoch * m + i)\n",
    "        theta = theta - eta * gradients\n",
    "        theta_path_sgd.append(theta)\n",
    "        \n",
    "print(theta)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[ 3.57214013] [ 3.39609675]\n"
     ]
    }
   ],
   "source": [
    "# SGD Regression using Scikit:\n",
    "\n",
    "from sklearn.linear_model import SGDRegressor\n",
    "\n",
    "sgd_reg = SGDRegressor(n_iter=50, penalty=None, eta0=0.1)\n",
    "sgd_reg.fit(X, y.ravel())\n",
    "\n",
    "print(sgd_reg.intercept_, sgd_reg.coef_)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[ 3.70412445]\n",
      " [ 3.54124923]]\n"
     ]
    }
   ],
   "source": [
    "# Gradient Descent - MiniBatch\n",
    "# adv: performance boost via GPUs\n",
    "\n",
    "theta_path_mgd = []\n",
    "\n",
    "n_iterations = 50\n",
    "minibatch_size = 20\n",
    "\n",
    "import numpy.random as rnd\n",
    "\n",
    "rnd.seed(42)\n",
    "theta = rnd.randn(2,1)  # random initialization\n",
    "\n",
    "t0, t1 = 10, 1000\n",
    "def learning_schedule(t):\n",
    "    return t0 / (t + t1)\n",
    "\n",
    "t = 0\n",
    "for epoch in range(n_iterations):\n",
    "    shuffled_indices = rnd.permutation(m)\n",
    "    X_b_shuffled = X_b[shuffled_indices]\n",
    "    y_shuffled = y[shuffled_indices]\n",
    "        \n",
    "    for i in range(0, m, minibatch_size):\n",
    "        t += 1\n",
    "        \n",
    "        xi = X_b_shuffled[i:i+minibatch_size]\n",
    "        yi =   y_shuffled[i:i+minibatch_size]\n",
    "        \n",
    "        gradients = 2 * xi.T.dot(xi.dot(theta) - yi)\n",
    "        eta = learning_schedule(t)\n",
    "        theta = theta - eta * gradients\n",
    "        theta_path_mgd.append(theta)\n",
    "        \n",
    "print(theta)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "theta_path_bgd = np.array(theta_path_bgd)\n",
    "theta_path_sgd = np.array(theta_path_sgd)\n",
    "theta_path_mgd = np.array(theta_path_mgd)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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OefPm4e3tzbp165g3b57efDs7OwIDA9m/fz++vr68ffuWkiVL8s0339CvXz82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\nIkVOCZ2IiIhIkfv/SCQDYuYTKfEAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f980e74ecc0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(10,4))\n",
    "plt.plot(theta_path_sgd[:, 0], theta_path_sgd[:, 1], \"r-s\", linewidth=1, label=\"Stochastic\")\n",
    "plt.plot(theta_path_mgd[:, 0], theta_path_mgd[:, 1], \"g-+\", linewidth=1, label=\"Mini-batch\")\n",
    "plt.plot(theta_path_bgd[:, 0], theta_path_bgd[:, 1], \"b-o\", linewidth=1, label=\"Batch\")\n",
    "plt.legend(loc=\"upper right\", fontsize=14)\n",
    "plt.xlabel(r\"$\\theta_0$\", fontsize=20)\n",
    "plt.ylabel(r\"$\\theta_1$   \", fontsize=20, rotation=0)\n",
    "plt.axis([2.5, 4.5, 2.3, 3.9])\n",
    "#save_fig(\"gradient_descent_paths_plot\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Polynomial Regression"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f980de24cc0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# example quadratic equation + noise: y = 0.5*X^2 + X + 2 + noise\n",
    "m = 100\n",
    "X = 6 * np.random.rand(m, 1) - 3\n",
    "y = 0.5 * X**2 + X + 2 + np.random.randn(m, 1)\n",
    "\n",
    "plt.scatter(X,y)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "PolynomialFeatures(degree=2, include_bias=False, interaction_only=False)\n",
      "[ 2.38942838] [ 2.38942838  5.709368  ]\n",
      "[ 1.9735233] [[ 0.95038538  0.52577032]]\n"
     ]
    }
   ],
   "source": [
    "# fit using Scikit\n",
    "\n",
    "from sklearn.preprocessing import PolynomialFeatures\n",
    "from sklearn.linear_model  import LinearRegression\n",
    "\n",
    "# caution: PolynomialFeatures converts array of n features\n",
    "# into array of (n+d)!/d!n! features -- combinatorial explosions possible :-)\n",
    "\n",
    "poly_features = PolynomialFeatures(degree=2, include_bias=False)\n",
    "print(poly_features)\n",
    "\n",
    "# X_poly: original feature of X, plus its square.\n",
    "X_poly = poly_features.fit_transform(X)\n",
    "\n",
    "#print(X, X_poly)\n",
    "print(X[0], X_poly[0])\n",
    "\n",
    "# fit it:\n",
    "lin_reg = LinearRegression()\n",
    "lin_reg.fit(X_poly, y)\n",
    "print(lin_reg.intercept_, lin_reg.coef_)\n",
    "\n",
    "# result estimate: 0.48x(1)^2 + 0.99x(2) + 2.06\n",
    "# original:        0.50x(1)^2 + 1.00x(2) + 2.00 + gaussian noise"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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P3sTExo1uXMsLL7jbw4bBQw+5ua1M0kmuEbk1kZ0Nn34Kw4e7Gs5FF7kh5WvX\n+l2yvbJ+9JWLxyjipBmpHF7N6oUXoHFjePppmDrVAr5JoBG5NdG0qfuyn3iiq/HMmuX+ER58EM46\ny+/SVckWn9jTpElueEZxsZt9O5ZnP+HURsuWbqr4hD7D2rYNrrnGvWEARx/tFizv2LHSzS2tk4Ii\n6eITz0vUXTYj9eOPqscd57qpgeoZZ6iuX+/NvmIg3I3Pus+596BOnbKPLi0tdl0ay3efzMhwrx2X\nbpPl9h+zz3nuXNUOHdwB1K2retddrktzNfu2rprJg5Tpshmpdu3cfOCPPOLmFvnvf+F3v3PXNWzX\n8DIVYItPlMnNdYs3haWnx+7sp3wqrbgY0tLi14slZpOpbdsGF1/spj5etcqtXZuf72r86VUPVLQ0\nYmpK7vRORSJujc/jjnMLs8yfD2eeCUOHugautm0jfilrbI2fnByX0ikocEH5gQdi915XTKXde6/r\nwu5luiOcUvn++xhMpvbaay51+eOPbt2Jm2+G6693f++FpRFTVCSnA/G8eJbeqai4WPXhh1UbN3an\nw02bqj7yiLs/AnEdQWk8TXfFM5VWPqVSr57LwtQovbJ+veqwYWU5r6ws1c8+q1F5LI2YHIgwveN7\nkK94iVvQD/vhB9UTTij75+nXT/WLL/b6NMuHmvIiDZ4VKwujR0cZdIuLVR99VLV5c/ciDRqoTpyo\n779TZME7xVnQj0YopDptmmrr1u4tqVNH9frrVX/9tdqnWS3JqEZXAahVZeGLL1SPOKKsgjJwoOqy\nZZ5XQOx7nhgs6NfEli2qF11UNnnb/vurTp/ufhTiwP65ElO0qb6oP+eff1a96qqyney3n+ozz5R+\nL71MNdoZbeKINOinVkPu3jRrRt5fHuIbRnDavItptPRjOP10N6/Pffe5BaI9Yg3DiSvaBtHs7Ag/\nW1X4z3/cHFLr1oEIa0+5iGd63EF2x2ZkS832Hw2vVu4yPorklyGeFz9r+uVrNZn1d+nyax4qy52m\np6tefrnqpk2e7NsahoMp0lp5zM/S8vJUDz+8LJWTna2fTV5UZa3bq7NEq+knDiy9E71KA+/69aqj\nRpWN2mnRQvVf/1ItKIjpvu2fK3h8+UxWrdq9V07r1qpPPqlaXOxbxcDSjokh0qCfOoOzIlDpFLOt\nWsHDD8Mnn0D//rB5M1x+uRvY9cILNR7YVZFXU+smzVwyPojr4KUtW1z/+kMOcbNg1qsHY8e6KZHP\nOw/S0nxY1/znAAAOyklEQVSbAtkGCiaZSH4Z4nnxtSFX91KrCYVUZ8xQ7dKlrCZ2+OGq8+fHu5gR\nsbOH2onL+7dzp+rdd5elEUH17LNVV66sskxW6zaVwdI7HiosVH3oIdV99y37Rz3uONWPPvK7ZLux\ndoLa8yzIFhS4wYHt2pV9h/r3D9x3yCSOSIN+8s6nHw/btrlx+xMnwtat7r6hQ2HcOOjVy9+yUXmP\nILBZFX1VVOSmOL71Vlixwt33hz/AHXfAn/+cEOs9mGCyRVTiadMmuPNOuP9+2LnT3Td0qJsHpXdv\nz3df3fS45R8D6xbqm6IieOopF9y/+87d16WLC/6nn+4mFTKmFiIN+r6ncypeEiK9U5U1a1Svvtol\ngMOn7IMHq77zjme7jCbvbOkeH2zfrnr//WVTHoNq586uR05Rkd+lqxFrVwgmkqn3TsL0QGnd2i3L\nuGIF/O//umUaZ892C1kceSS8/PLucwTHQDQ9TIKyAHbCfJ61sXkz3H47dOjg1qddtQq6dnWDrZYs\ncT1y6iTe2MiYTQdt/BPJL0M8LxVr+gndA2XjRtVx43bvmdG5s2sE3r49JruI9v3xu5aW0J9nJJYu\ndVN5lD/by8pSfeGFahc0CavtYDCvP187WwwugtJ7B9gfmA98BXwJXFHd9hWDflJ8ybZuVb3nnt1P\n8Zs3V73mGtXvvqv1y/sdyKORFJ9nRcXFqrNmqR5/fNm8TaA6aJBbzSrCuZsi/UGsart4/KAm/Y92\nAos06McjvbML+F9V7Q4cDlwiIt0jfXJQUhK10rixW3x12TJ47jk47DA3GGfiRDjoIDjpJLcYRnFx\n6VOiSYEk0uCZpPg8wzZtgnvuYWeHLq7nzWuvuYO68EJYvNil9gYMiLhHTqSpuqq2i8dgMq8GEZo4\niuSXIZYX4GXg2Koer6whN5FqshH74APVv/zFraIRrhnuv7/qP/6h+S+uSuraVEJ/nsXFqvPmqZ5z\nzm6f3UoO0JvqjNcPX6v5usuJUNM3wUUQ++mLSEfgHaCHqm6tbJu9ddmsrntiQlq3DqZMgUcfheXL\nAVAR3tIBTGEEL6edyo23N2TMGH+LmfKWL3ddLp9+uqx/vQjLOw/i2mWjeDl0IpKezm23UavPKtLv\nd3i7li13X94x6f4/TMQC12UTaAQsAk6t5LGRQD6Qf8ABB1T5S5bUNZniYpf/PessLa5br7QGuY1M\nXX/cuaqvveZGApv4WbvWdbfs16/sbAxU27dXvflm1ZUrff1OJvX/g4kaQZpPX0QygBeAqar6YiU/\nPJOASeBq+lW9TlLP7Z2W5vK/AwaQtmULy//5PPWfnUy7Hz6g0RtT4Y2prlp38slw2mlu27p1/S51\n8lm7FmbMcJPpzZtX1sW2YUP3vo8Y4SbeKxlMld3B5bb9qF0n9f+D8Yzn6R0REeBJYLOqXrm37atL\n7wRloZG4nkIvWwbTprmZF5csKbu/aVMYMgROPBEGD4bmzT0uSJJSha+/hldfdeMo3n+/bObUjAz3\n3p59tmtsb9TI37JWEJT/BxMMgZmGQUSOBBYAXwDhkUk3qurrlW0f9Jy+b/9oqvDll64GOn266x0S\nlp7uBn8NGuQuhx5qw/qrs22b+xK98Qa8/nrZtAjgpjQ+7jg45RQ3lUaLFr4VMxJ+/z+Y4AhM0I9W\n0OfeGT/ejUYsLnaxtrYNdzX27bcwc6a7LFiwW3dPWrVyUSB86dYttSfy2rHDRce334b582HhQti1\nq+zxffZxXS5POMFdN27sX1mNqSEL+h4J5Cn1zz/D3Lmu5jpnDnz//e6Pt2zpCtmvn7vu3RuaNPGn\nrF5Tdcf/wQfuw1q4EBYtchOehaWnQ9++bu3jQYPcuIn0dP/KbEwMWND3UKBPqVXdWUBuLuTmUvjG\nfOpuWrvndoccAllZblrfnj3dpV27Ss8IAnu8hYWwdKlLdX3+OXz8sbts3Lj7dmlpLuX1pz+VXZo1\n86fMxnjEgr5xZyXHKG0LV3JU+vuMP/F9Wq/6wAXI8jXfsCZN3HS/hxzirjt1YvH2Tpx8ZUe+L2xN\nnXrp8T+z2bHD1dxXrYKVK90P2rffumUEly3bPU0T1qKFq8lnZ7tL376u4duYJBZp0E+8af4SWLxr\nzLm5UFgkLA91YqV04pCscxnzAq6GvHixS3t8/jl88YW7bN4MH33kLiV6AMuAXaSzdmdr0s5sC71a\nuzx4y5bu0rSpy4M3aeK6Ntat6xpE69YtO3MQcQG6sNBddu6EX391jarbtrl9b97sRhqtWwdr1rjL\nli1VH6AIHHww9OjhLr17u8sBB4BI2fvdKGBnKMb4yIJ+nPjRFhCe5ya8z9J5burWLQuQYaqwYYNL\nlyxd6mrTK1eybfFKdn61gn3ZQHtWw4+r4Udvy72bjAwXxDt0cJfOnd3lkENcwG/YsNKnxeP9Dmza\ny5hqWNCPEz8G0oQnx4ooMInAvvu6y1FHld7dGFicB1PmFjDgd2vp03aNG8C0aZPLnW/cWFZb37rV\n1eALCtylsNC9SHgsa0aGi8DhM4HGjV3f90aNXEomfOaw777Qpo1bn2CffWrU/dTr9zuQDfrGRMCC\nfpxUWev2WDitXfvXqAd0KLkEn9fvt42GNYnKgn6cRFXrNrXm9fvt14+4MbVlvXeM5aZryN43EyTW\ne8dExHLTNReL1Jkx8WYTtKS4eKy2ZJyUWBDeBJ7V9FOc5abjw86oTFBYTT/FRbvmqRe11VSoAdsZ\nlQkKq+mb0kAfDkRVBX4vaquTJsGll7pgWK9e8taA7YzKBIUF/RpKpp4bkQbzSPqmR/O+5OXBJZeU\nTZ9TUJC8/d2ty64JCgv6NZBs+dlIBxrtrbYa7fuSm1u2GiG42Y2jqQEn2g9vxd4+iVZ+kxws6NdA\nso3GjDT1sLfaarTvS06OS+kUFLiZFh54IPL3MdF/eBO9/CZxWdCvgWTLz0aTeqiub3q070ttUh6J\n/sOb6OU3icuCfg3EIj8btFP7WM3RU/F92dtx1nS/QfjhLX9sEN3nGYTym9Rk0zD4IBFO7WPxo+T1\ncfr5w1n+2NLTy5YLiOY4g/bDbxKbTcMQYEE/tY9VsPb6OP2cBqH8sYUbo1WjO06bxsH4wQZn+SB8\nap+eHsxT+1gNJAr6cdZG+WMLLxOQjMdpko/V9H0Q9D7bsco3J2PbR1jFY4NgltOYiiynn0RiGSCD\nEGwToe3DmKCwnH6KiXWADEK+OehtH8YkIsvpJ4mgTOgVy8nTkrlNwBi/WE0/SQSh37cXZxtBbvsw\nJhFZ0E8SQQiQXqRjgpBmMiaZWNBPIn4HyCCcbRhjqmdB38RMEM42jDHVs6BvYsrvsw1jTPWs944x\nxqQQC/rGGJNCLOgbY0wKsaBvjDEpJC5BX0QGi8hSEVkmIjfEY5/GGGP25HnQF5F04EHgz0B34BwR\n6e71fo0xxuwpHjX9vsAyVf1OVQuBacDQOOzXGGNMBfHop98O+KHc7R+Bw8pvICIjgZElNwtEZHEc\nyuWXfYCNfhfCQ3Z8iS2Zjy+Zjw2gSyQbBWJwlqpOAiYBiEh+JHNCJyo7vsRmx5e4kvnYwB1fJNvF\nI72zGti/3O32JfcZY4yJs3gE/Y+AziLSSUTqAmcDr8Rhv8YYYyrwPL2jqrtE5FJgDpAOPKGqX1bz\nlElel8lndnyJzY4vcSXzsUGExxe4NXKNMcZ4x0bkGmNMCrGgb4wxKSSQQV9EbhORz0XkUxF5Q0Ta\n+l2mWBKRu0Tk65JjfElEmvldplgSkTNE5EsRCYlIUnSRS+apRETkCRFZn6zjY0RkfxGZLyJflXwv\nr/C7TLEkIvVF5EMR+azk+P5R7fZBzOmLSBNV3Vry9+VAd1Ud7XOxYkZEjgPmlTRyTwBQ1et9LlbM\niEg3IAQ8AlyjqhH1Hw6qkqlEvgGOxQ0u/Ag4R1W/8rVgMSIiRwO/Ak+pag+/yxNrItIGaKOqH4tI\nY2ARcHISfX4CZKrqryKSAbwLXKGqCyvbPpA1/XDAL5EJBO+XqRZU9Q1V3VVycyFu7ELSUNUlqrrU\n73LEUFJPJaKq7wCb/S6HV1R1jap+XPL3NmAJbqaApKDOryU3M0ouVcbMQAZ9ABH5fyLyA3AucLPf\n5fHQ34BZfhfCVKuyqUSSJmikEhHpCPQCPvC3JLElIuki8imwHnhTVas8Pt+CvojMFZHFlVyGAqjq\nWFXdH5gKXOpXOWtqb8dXss1YYBfuGBNKJMdnTJCISCPgBeDKCtmEhKeqxap6KC5r0FdEqkzT+Tb3\njqoOjHDTqcDrwDgPixNzezs+ETkfOAEYoEFsWNmLKD6/ZGBTiSS4klz3C8BUVX3R7/J4RVV/FpH5\nwGCg0ob5QKZ3RKRzuZtDga/9KosXRGQwcB1wkqru8Ls8Zq9sKpEEVtLQ+TiwRFX/z+/yxJqItAr3\nABSRBrgOB1XGzKD23nkBN01oCFgFjFbVpKlZicgyoB6wqeSuhUnWO+kU4H6gFfAz8KmqDvK3VLUj\nIkOAeymbSuT/+VykmBGRZ4Ec3NTD64Bxqvq4r4WKIRE5ElgAfIGLKQA3qurr/pUqdkTk98CTuO9m\nGvC8qt5a5fZBDPrGGGO8Ecj0jjHGGG9Y0DfGmBRiQd8YY1KIBX1jjEkhFvSNMSaFWNA3xpgUYkHf\nmEqIyOkiUiAiHcrdd5+ILBeR/fwsmzG1Yf30jalEySjOj4BPVPV/ROQa3CjqI1T1W39LZ0zN+Tb3\njjFBpqoqIjcCr4nIcuBG3DxJ3wKIyEu4Uaxvqerp/pXUmOhYTd+YaojI+7j59E9U1Vnl7s8BGgMj\nLOibRGI5fWOqICLHAH8ABDcnTSlVzQW2+VAsY2rFgr4xlRCRPwAvAZcBM4Dx/pbImNiwnL4xFZT0\n2JkF3K2qT4jIh8DnIpJTUsM3JmFZTd+YckSkBTAbmBmenlZVFwP/xWr7JglYTd+YclR1M9CtkvvP\n8qE4xsSc9d4xpgZEZC6ukTcT2Aycoap5/pbKmL2zoG+MMSnEcvrGGJNCLOgbY0wKsaBvjDEpxIK+\nMcakEAv6xhiTQizoG2NMCrGgb4wxKcSCvjHGpBAL+sYYk0L+P5qM1aRRI6+IAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f980dd31c50>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "X_new      = np.linspace(-3, 3, 100).reshape(100, 1)\n",
    "X_new_poly = poly_features.transform(X_new)\n",
    "y_new      = lin_reg.predict(X_new_poly)\n",
    "\n",
    "#testme = np.linspace(-3,3,20)\n",
    "#print(testme, testme.reshape(20,1))\n",
    "\n",
    "plt.plot(X, y, \"b.\")\n",
    "plt.plot(X_new, y_new, \"r-\", linewidth=2, label=\"Predictions\")\n",
    "plt.xlabel(\"$x_1$\", fontsize=14)\n",
    "plt.ylabel(\"$y$\", rotation=0, fontsize=14)\n",
    "plt.legend(loc=\"upper left\", fontsize=14)\n",
    "plt.axis([-3, 3, 0, 10])\n",
    "#save_fig(\"quadratic_predictions_plot\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Learning Curves"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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GBW3vEOBp3M08f/TNf973Gc/B3a7lReAdEWkX5bOa8iTZ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\nYgnDGGOMJ5YwjDHGePL/cpSTX2c3xnAAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f980e7645c0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# another way to check for underfit & overfit:\n",
    "# use learning curve plots to see performance vs training set size.\n",
    "\n",
    "from sklearn.metrics import mean_squared_error\n",
    "from sklearn.model_selection import train_test_split\n",
    "\n",
    "# train model multiple times on various training subsets (of various sizes)\n",
    "\n",
    "def plot_learning_curves(model, X, y):\n",
    "    X_train, X_val, y_train, y_val = train_test_split(X, y, test_size=0.2, random_state=10)\n",
    "    train_errors, val_errors = [], []\n",
    "    for m in range(1, len(X_train)):\n",
    "        model.fit(X_train[:m], y_train[:m])\n",
    "        y_train_predict = model.predict(X_train[:m])\n",
    "        y_val_predict = model.predict(X_val)\n",
    "        train_errors.append(mean_squared_error(y_train_predict, y_train[:m]))\n",
    "        val_errors.append(mean_squared_error(y_val_predict, y_val))\n",
    "\n",
    "    plt.plot(np.sqrt(train_errors), \"r-+\", linewidth=2, label=\"Training set\")\n",
    "    plt.plot(np.sqrt(val_errors), \"b-\", linewidth=3, label=\"Validation set\")\n",
    "    plt.legend(loc=\"upper right\", fontsize=14)\n",
    "    plt.xlabel(\"Training set size\", fontsize=14)\n",
    "    plt.ylabel(\"RMSE\", fontsize=14)\n",
    "\n",
    "lin_reg = LinearRegression()\n",
    "plot_learning_curves(lin_reg, X, y)\n",
    "plt.axis([0, 80, 0, 3])\n",
    "#save_fig(\"underfitting_learning_curves_plot\")\n",
    "plt.show()\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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iTxxJSe4lxcOH3Q3+4ovdzTDHrl1w4on+ThGHDXPNjcuUcdd/4w3X5DS4A8ii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\n/w/wE18KcZc4GwAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f980dcfc550>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# repeat exercise for 10th-degree polynomial\n",
    "\n",
    "from sklearn.pipeline import Pipeline\n",
    "\n",
    "polynomial_regression = Pipeline((\n",
    "    (\"poly_features\", PolynomialFeatures(degree=10, include_bias=False)),\n",
    "    (\"sgd_reg\", LinearRegression()),\n",
    "))\n",
    "\n",
    "plot_learning_curves(polynomial_regression, X, y)\n",
    "plt.axis([0,80,0,3])\n",
    "plt.show()\n",
    "\n",
    "# note: training error rate much lower than on Linear Regression\n",
    "# note: training/validation gap closes to zero. good fit?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Bias/Variance Tradeoff\n",
    "\n",
    "* Bias: the part of generalization error due to wrong assumptions.\n",
    "* Variance: due to model sensitivity to small training variations. (More common in high-dimensional models.)\n",
    "* Irreducibility: due to data noise.\n",
    "\n",
    "* Rule of thumb: increasing model complexity increases variance & reduces bias (and vice versa.)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Regularization\n",
    "\n",
    "* Used to reduce overfit by constraining the model (ex: reducing the # of degrees in a polynomial)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# Ridge -- regularization term added to cost function.\n",
    "# alpha param -- forces model weights to minimal values. higher alpha = \"flatter\" function (converge to mean)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "* Cost function:\n",
    "![ridge-regression-cost-function](pics/ridge-regression-cost-function.png)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 1.00650911],\n",
       "       [ 1.55071465],\n",
       "       [ 1.73211649],\n",
       "       [ 2.09492018]])"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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ZJPuAB4FdixVMcgA4ALBz587R1VCSplyXVwwvADvmvd7ebPtrVXW6qs40zw8Dm5NsWezD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\nUovBIElqMRgkSS0GgySp5f8DLm3GQEg8GJYAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f9825c75f60>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# build dataset\n",
    "\n",
    "import numpy.random as rnd\n",
    "\n",
    "rnd.seed(42)\n",
    "m = 20\n",
    "X = 3 * rnd.rand(m, 1)\n",
    "y = 1 + 0.5 * X + rnd.randn(m, 1) / 1.5\n",
    "X_new = np.linspace(0, 3, 100).reshape(100, 1)\n",
    "\n",
    "# plot it\n",
    "plt.plot(X, y, \"b.\")\n",
    "plt.xlabel(\"$x_1$\", fontsize=18)\n",
    "plt.ylabel(\"$y$\", rotation=0, fontsize=18)\n",
    "plt.axis([0, 3, 0, 4])\n",
    "\n",
    "# apply Ridge regression\n",
    "from sklearn.linear_model import Ridge\n",
    "\n",
    "ridge_reg = Ridge(alpha=1, solver=\"cholesky\")\n",
    "ridge_reg.fit(X,y)\n",
    "ridge_reg.predict([[0.0],[1.5],[2.0],[3.0]])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 1.00650911],\n",
       "       [ 1.55071465],\n",
       "       [ 1.73211649],\n",
       "       [ 2.09492018]])"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Ridge using SGD:\n",
    "sgd_reg = SGDRegressor(penalty=\"l2\") \n",
    "sgd_reg.fit(X,y.ravel())\n",
    "ridge_reg.predict([[0.0],[1.5],[2.0],[3.0]])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 1.14537356,  1.53788174,  1.66871781,  1.93038993])"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Lasso -- similar to Ridge, also adds regularization term\n",
    "# uses L1 norm (instead of 1/2 square of L2 norm, as in Ridge.)\n",
    "# -- tends to force least important features to zero.\n",
    "\n",
    "from sklearn.linear_model import Lasso\n",
    "\n",
    "lasso_reg = Lasso(alpha=0.1)\n",
    "lasso_reg.fit(X,y)\n",
    "lasso_reg.predict([[0.0],[1.5],[2.0],[3.0]])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 1.08639303,  1.54333232,  1.69564542,  2.00027161])"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Elastic Net -- midddle ground.\n",
    "# regularization = mix of Ridge & Lasso (mix ratio \"r\")\n",
    "\n",
    "from sklearn.linear_model import ElasticNet\n",
    "\n",
    "elastic_net = ElasticNet(alpha=0.1, l1_ratio=0.5)\n",
    "elastic_net.fit(X,y)\n",
    "elastic_net.predict([[0.0],[1.5],[2.0],[3.0]])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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paUEuXykzbdo0BXTdunWalpamR44c0Z9//ll79OihtWrV0v3792eeu2zZMq1S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\nE5AFCWOMMQH9P9YSwqpZNS0iAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f980dd3b0b8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Early Stopping -- stop training when minimum validation error reached\n",
    "\n",
    "# build dataset\n",
    "rnd.seed(42)\n",
    "m = 100\n",
    "X = 6 * rnd.rand(m, 1) - 3\n",
    "y = 2 + X + 0.5 * X**2 + rnd.randn(m, 1)\n",
    "\n",
    "X_train, X_val, y_train, y_val = train_test_split(X[:50], y[:50].ravel(), test_size=0.5, random_state=10)\n",
    "\n",
    "from sklearn.preprocessing import StandardScaler\n",
    "from sklearn.pipeline import Pipeline\n",
    "\n",
    "poly_scaler = Pipeline((\n",
    "    (\"poly_features\", PolynomialFeatures(\n",
    "        degree=90, \n",
    "        include_bias=False)),\n",
    "    (\"std_scaler\", StandardScaler()),\n",
    "    ))\n",
    "\n",
    "X_train_poly_scaled = poly_scaler.fit_transform(X_train)\n",
    "X_val_poly_scaled   = poly_scaler.transform(X_val)\n",
    "\n",
    "sgd_reg = SGDRegressor(n_iter=1,\n",
    "                       penalty=None,\n",
    "                       eta0=0.0005,\n",
    "                       warm_start=True,\n",
    "                       learning_rate=\"constant\",\n",
    "                       random_state=42)\n",
    "\n",
    "n_epochs = 500\n",
    "train_errors, val_errors = [], []\n",
    "\n",
    "for epoch in range(n_epochs):\n",
    "    sgd_reg.fit(X_train_poly_scaled, y_train)\n",
    "\n",
    "    y_train_predict = sgd_reg.predict(X_train_poly_scaled)\n",
    "    y_val_predict   = sgd_reg.predict(X_val_poly_scaled)\n",
    "\n",
    "    train_errors.append(mean_squared_error(y_train_predict, y_train))\n",
    "    val_errors.append(mean_squared_error(y_val_predict, y_val))\n",
    "\n",
    "best_epoch    = np.argmin(val_errors)\n",
    "best_val_rmse = np.sqrt(val_errors[best_epoch])\n",
    "\n",
    "plt.annotate('Best model',\n",
    "             xy=(best_epoch, best_val_rmse),\n",
    "             xytext=(best_epoch, best_val_rmse + 1),\n",
    "             ha=\"center\",\n",
    "             arrowprops=dict(facecolor='black', shrink=0.05),\n",
    "             fontsize=16,\n",
    "            )\n",
    "\n",
    "best_val_rmse -= 0.03  # just to make the graph look better\n",
    "plt.plot([0, n_epochs], [best_val_rmse, best_val_rmse], \"k:\", linewidth=2)\n",
    "plt.plot(np.sqrt(val_errors), \"b-\", linewidth=3, label=\"Validation set\")\n",
    "plt.plot(np.sqrt(train_errors), \"r--\", linewidth=2, label=\"Training set\")\n",
    "plt.legend(loc=\"upper right\", fontsize=14)\n",
    "plt.xlabel(\"Epoch\", fontsize=14)\n",
    "plt.ylabel(\"RMSE\", fontsize=14)\n",
    "#save_fig(\"early_stopping_plot\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Logistic Regression\n",
    "* commonly used to est probability of instance belonging to specified class. positive if >50% (labeled \"1\"), otherwise labeled \"0\".\n",
    "\n",
    "![Logistic Regression model probability](logistic-regression-probability.png)\n",
    "\n",
    "* logistic is a sigmoid function, outputs 0<n<1.\n",
    "\n",
    "![Logistic function](logistic-function.png)\n",
    "\n",
    "* cost function = average over all training data. It is convex, so gradient descent will find global minimum."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "dict_keys(['target_names', 'DESCR', 'data', 'target', 'feature_names'])\n"
     ]
    }
   ],
   "source": [
    "#from sklearn import datasets\n",
    "#iris = datasets.load_iris()\n",
    "\n",
    "import numpy as np\n",
    "\n",
    "from sklearn import datasets\n",
    "iris = datasets.load_iris()\n",
    "print(iris.keys())\n",
    "\n",
    "X = iris[\"data\"][:, 3:] # petal width\n",
    "y = (iris[\"target\"] == 2).astype(np.int) # 1 if Iris-Virginica, else 0"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[ 0.98552764  0.01447236]\n",
      " [ 0.98541511  0.01458489]\n",
      " [ 0.98530171  0.01469829]\n",
      " ..., \n",
      " [ 0.02620686  0.97379314]\n",
      " [ 0.02600703  0.97399297]\n",
      " [ 0.02580868  0.97419132]]\n"
     ]
    },
    {
     "data": {
      "image/png": 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C8+Yy35MpRUZH0vaPtiw7toxJDSYxrOYwc4ckUpk0XItMqXNno/rJwsL4Kd7cw8cPabWk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\nniScc86l9H9fMjPXbxyVAAAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f980cecffd0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# train a LR model\n",
    "\n",
    "from sklearn.linear_model import LogisticRegression\n",
    "log_reg=LogisticRegression()\n",
    "log_reg.fit(X,y)\n",
    "\n",
    "# predict probability of flowers with petal widths = 0-3cm \n",
    "X_new             = np.linspace(0, 3, 1000).reshape(-1, 1)\n",
    "y_proba           = log_reg.predict_proba(X_new)\n",
    "print(y_proba)\n",
    "decision_boundary = X_new[y_proba[:, 1] >= 0.5][0]\n",
    "\n",
    "plt.plot(X_new, y_proba[:, 1], \"g-\", label=\"Iris-Virginica\")\n",
    "plt.plot(X_new, y_proba[:, 0], \"b--\", label=\"Not Iris-Virginica\")\n",
    "plt.text(decision_boundary+0.02, 0.15, \"Decision  boundary\", fontsize=14, color=\"k\", ha=\"center\")\n",
    "plt.xlabel(\"Petal width (cm)\", fontsize=14)\n",
    "plt.ylabel(\"Probability\", fontsize=14)\n",
    "plt.legend(loc=\"center left\", fontsize=14)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[0 1]\n"
     ]
    }
   ],
   "source": [
    "# what's the prediction for petal length = 1.5 or 1.7cm?\n",
    "print(log_reg.predict([[1.5], [1.7]]))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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3sy/0XZv0rHSS1cnYmdn9q9glSd5mzcObnsx16gTh4boNio8dAwMD2LABSpV6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\nzIs555xzzrkM5sWcc84551wG+3+SFi5K2+3VdQAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f980cbd10f0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Logistic Regressin contour plot\n",
    "# with multiple decision boundaries (not just 50%)\n",
    "\n",
    "from sklearn.linear_model import LogisticRegression\n",
    "\n",
    "X = iris[\"data\"][:, (2, 3)]  # petal length, petal width\n",
    "y = (iris[\"target\"] == 2).astype(np.int)\n",
    "\n",
    "log_reg = LogisticRegression(C=10**10)\n",
    "log_reg.fit(X, y)\n",
    "\n",
    "x0, x1 = np.meshgrid(\n",
    "         np.linspace(2.9, 7, 500).reshape(-1, 1),\n",
    "         np.linspace(0.8, 2.7, 200).reshape(-1, 1),\n",
    "    )\n",
    "\n",
    "# ravel(): return contiguous flattened array\n",
    "X_new = np.c_[x0.ravel(), x1.ravel()]\n",
    "\n",
    "y_proba = log_reg.predict_proba(X_new)\n",
    "\n",
    "plt.figure(figsize=(10, 4))\n",
    "plt.plot(X[y==0, 0], X[y==0, 1], \"bs\")\n",
    "plt.plot(X[y==1, 0], X[y==1, 1], \"g^\")\n",
    "\n",
    "zz = y_proba[:, 1].reshape(x0.shape)\n",
    "contour = plt.contour(x0, x1, zz, cmap=plt.cm.brg)\n",
    "\n",
    "\n",
    "left_right = np.array([2.9, 7])\n",
    "boundary = -(log_reg.coef_[0][0] * left_right + log_reg.intercept_[0]) / log_reg.coef_[0][1]\n",
    "\n",
    "plt.clabel(contour, inline=1, fontsize=12)\n",
    "plt.plot(left_right, boundary, \"k--\", linewidth=3)\n",
    "plt.text(3.5, 1.5, \"Not Iris-Virginica\", fontsize=14, color=\"b\", ha=\"center\")\n",
    "plt.text(6.5, 2.3, \"Iris-Virginica\", fontsize=14, color=\"g\", ha=\"center\")\n",
    "plt.xlabel(\"Petal length\", fontsize=14)\n",
    "plt.ylabel(\"Petal width\", fontsize=14)\n",
    "plt.axis([2.9, 7, 0.8, 2.7])\n",
    "#save_fig(\"logistic_regression_contour_plot\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "### Softmax Regression (Multinomial Logistic Regression)\n",
    "\n",
    "* **Predicts one class at a time (multiclass, not multioutput). Use only for mutually exclusive classes.**\n",
    "* Scoring for K classes: ![softmax-score-for-class K](pics/softmax-score-for-class-k.png)\n",
    "* Softmax function (aka normalized exponential):    ![softmax-function](softmax-function.png)\n",
    "* Prediction: ![softmax prediction](pics/softmax-prediction.png)\n",
    "* Uses **cross entropy** to minimize cost function. (Same as log loss, used for Logistic Regression, when k=2.)\n",
    "![cross entropy](pics/cross-entropy-cost-function.png)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[  6.33134078e-07,   5.75276067e-02,   9.42471760e-01]])"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# use Softmax to classify iris flowers\n",
    "\n",
    "X = iris[\"data\"][:, (2, 3)] # petal length, width\n",
    "y = iris[\"target\"]\n",
    "\n",
    "# Scikit LR can be switched to Softmax with \"multinomial\" setting.\n",
    "# also defaults to L2 regularization (control with C parameter)\n",
    "\n",
    "softmax_reg = LogisticRegression(multi_class=\"multinomial\",solver=\"lbfgs\", C=10)\n",
    "softmax_reg.fit(X, y)\n",
    "\n",
    "# predict iris 5cm long, 2cm wide:\n",
    "\n",
    "softmax_reg.predict([[5, 2]])\n",
    "softmax_reg.predict_proba([[5,2]])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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S4v0FzSZvxmFrIpivnUDtAgQBS7W0P6bD4yE1GT+aORhu4NgEA3mHrXtjNDozfe4/zrwj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\nV1qqgX9M4+k5G2SYYMMwrPgfcdJCYphJhGhMtGVb7C2nMHl0fe6nZux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2gKQ4VYH9Dbw4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jP+k4NcjLPlg/v68UGfPsTsczL7PbrbkSejysjc4ahMnMUJxnmcprk4S2vQTKz6FWjqaNRTaQRN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\nTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f980c86c9b0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# softmax contour plot\n",
    "\n",
    "x0, x1 = np.meshgrid(\n",
    "        np.linspace(0, 8, 500).reshape(-1, 1),\n",
    "        np.linspace(0, 3.5, 200).reshape(-1, 1),\n",
    "    )\n",
    "X_new = np.c_[x0.ravel(), x1.ravel()]\n",
    "\n",
    "\n",
    "y_proba = softmax_reg.predict_proba(X_new)\n",
    "y_predict = softmax_reg.predict(X_new)\n",
    "\n",
    "zz1 = y_proba[:, 1].reshape(x0.shape)\n",
    "zz = y_predict.reshape(x0.shape)\n",
    "\n",
    "plt.figure(figsize=(10, 4))\n",
    "plt.plot(X[y==2, 0], X[y==2, 1], \"g^\", label=\"Iris-Virginica\")\n",
    "plt.plot(X[y==1, 0], X[y==1, 1], \"bs\", label=\"Iris-Versicolor\")\n",
    "plt.plot(X[y==0, 0], X[y==0, 1], \"yo\", label=\"Iris-Setosa\")\n",
    "\n",
    "from matplotlib.colors import ListedColormap\n",
    "custom_cmap = ListedColormap(['#fafab0','#9898ff','#a0faa0'])\n",
    "\n",
    "plt.contourf(x0, x1, zz, cmap=custom_cmap, linewidth=5)\n",
    "contour = plt.contour(x0, x1, zz1, cmap=plt.cm.brg)\n",
    "plt.clabel(contour, inline=1, fontsize=12)\n",
    "plt.xlabel(\"Petal length\", fontsize=14)\n",
    "plt.ylabel(\"Petal width\", fontsize=14)\n",
    "plt.legend(loc=\"center left\", fontsize=14)\n",
    "plt.axis([0, 7, 0, 3.5])\n",
    "#save_fig(\"softmax_regression_contour_plot\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "celltoolbar": "Raw Cell Format",
  "kernelspec": {
   "display_name": "Python [Root]",
   "language": "python",
   "name": "Python [Root]"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.5.2"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}
